UNIVERSITI KUALA LUMPUR Malaysia France Institute
FINAL EXAMINATION SEPTEMBER 2013 SESSION
SUBJECT CODE : FAB 30803
SUBJECT TITLE : CONTROL SYSTEM
LEVEL : BACHELOR
TIME / DURATION :
( 3 HOURS )
DATE :
INSTRUCTIONS TO CANDIDATES
1. Please read the instructions given in the question paper CAREFULLY.
2. This question paper is printed on both sides of the paper.
3. Please write your answers on the answer booklet provided.
4. Answer should be written in blue or black ink except for sketching, graphic and illustration.
5. This question paper consists of SIX (6) questions. Answer FIVE (5) questions only.
6. Answer all questions in English.
7. The semi-log paper, Nichol’s chart, graph paper and formula are appended.
Question 1
(a) Analysis of a system can be done by studying the transient response, the steady state response and stability. Describe transient response, steady state response and stability of a system.
(3 marks) (b) Describe an example of close loop system in our home appliance.
(2 marks) (c) An automobile driver uses a control system to maintain the speed of the car at a
prescribed level. Draw a functional block diagram of a system.
(4 marks) (d) Figure 1 is a schematic diagram of a water flow control system. Draw the transfer
function, ) (
) (
s i
O s
.(11 marks)
Figure 1: An electromechanical open-loop control system
where,
Ka – amplifier gain constant Km - motor torque constant Kb – back emf constant K – potentiometer constant
J – inertia D – viscous friction
(a) Find the transfer function, ) (
) (
s R
s
C for the block diagram of a system in Figure 2 by using the block diagram reduction method.
(10 marks)
Figure 2: A block diagram of a system
(b) Referring to a block diagram of a unity feedback system shown in Figure 3, determine the natural frequency (ωn), damping ratio (ζ), settling time (Ts) and peak time (Tp).
(4 marks)
Figure 3: A block diagram of a unity feedback system
(c) For a closed loop control system shown in Figure 4, determine the values of K and T, if the percent overshoot, %OS = 20% and peak time, Tp = 2 seconds.
(6 marks)
Figure 4: A closed-loop control system
Question 3
(a) Figure 5 shows a signal flow graphs of a system. Obtain the overall transfer function, )
( ) (
s R
s
C of the system by using Mason’s rule formula.
(10 marks)
Figure 5: A flow graph of a system
(b) Consider the open loop transfer function of a unity feedback system as follows
) 23 12 6
2 (
) 25 ( ) 2
(
4 3 2
s s
s s s s s
G
i. Find the number of right half plane poles, left half plane poles and on imaginary axis poles using the Routh-Hurwitz Criterion.
(8 marks) ii. Determine the stability of the closed-loop system.
(2 marks)
Question 4
(a) The block diagram of an electric cart steering system is shown in Figure 6.
Figure 6: Electric cart steering system
i. Plot the asymptotic Bode diagram for the system if given thatK3.2.
(10 marks)
R(s) C(s) )
1 1 . 0 ( s
K
) 2 (
1
2s s +
-
cross over frequency (ωgco), phase cross over frequency (ωpco), and hence state and justify the stability of the system.
(5 marks) (b) An engineer has found the frequency response of an open loop system and tabulated
it as shown in Table 1.
Table 1: The data of an open loop system.
ω (rad/s) 0.2 0.3 0.5 0.8 1.2 1.4 1.8 2.0 2.5 3.0
|G|dB 17 13 9 4 1 0 -3 -4 -7 -10
G
-90 -100 -104 -105 -108 -111 -115 -120 -125 -130 i. Sketch the Nichols plot on the Nichols chart.
(3 marks) ii. Determine from the Nichol chart, the resonant peak and the bandwidth of the
closed loop system.
(2 marks)
Question 5
(a) A block diagram of a unity feedback system shows in Figure 7 is referred.
i. Determine the system type
(1 mark) ii. Find the value of
K
if the steady state error is 10%(3 marks) iii. Find the static error constants and steady state errors for inputs of
) ( 15 ), (
5u t tu t and 24t2u(t)for K100.
(6 marks)
Figure 7: A unity feedback of a closed loop system
(b) Consider a unity feedback of a system shown in Figure 8. Obtain the followings by using the Nyquist criterion.
i. Sketch the Nyquist plot of the system for (0<ω<∞)
(8 marks) ii. Determine the system stability of the system
(2 marks)
Figure 8: A unity feedback of a system
Question 6
(a) The block diagram of a unity feedback closed loop system is shown in Figure 9.
Figure 9: Unity feedback closed-loop system
i. Sketch the root locus of the closed loop system as K varies from zero to infinities, in the s-plane. Indicate the asymptotes, break points on the real axis, cross-over points at the imaginary axis, angle of departure or arrival, where appropriate.
(15 marks) ii. Determine the maximum damping ratio, of the stable complex closed loop pole.
(5 marks)
END OF QUESTION
